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Interpolation and compactness in categories of pre-institutions. (English) Zbl 0860.03035
The relationship between compactness, Craig interpolation and Robinson joint consistency were investigated by Makowsky, Shelah, as well as by the reviewer, and others, in the late seventies and in the eighties. The book: Model-theoretic logics (1985; Zbl 0587.03001 and Zbl 0587.03002) (edited by J. Barwise and S. Feferman) gives a comprehensive overview of the subject. An even more general set-up was introduced by the reviewer in his paper “A generalization of abstract model theory” [Fundam. Math. 124, 1-25 (1984; Zbl 0595.03039)]. In the paper under review the authors further analyze compactness, interpolation and other related model-theoretic properties, working in the context of pre-institutions. The latter were introduced in an earlier paper by the same authors, generalizing the notion of institution, due to Goguen and Burstall. Categories of pre-institutions allow a model-free generalization of the above mentioned notions. For their analysis the authors introduce appropriate analogues of ultraproducts, and prove a generalization of Łos’ theorem.
Reviewer: D.Mundici (Milano)

##### MSC:
 03C95 Abstract model theory 03G30 Categorical logic, topoi
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##### References:
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